Obliczamy:

$\left(\begin{array}{c}13\\ 2\end{array}\right)=\frac{13!}{2!\cdot \left(13-2\right)!}=\frac{13!}{2!\cdot 11!}=\frac{{\cancel{11!}}^1\cdot {\cancel{12}}^6\cdot 13}{1\cdot {\cancel{2}}^1\cdot {\cancel{11!}}^1}=78$  

$\left(\begin{array}{c}13\\ 3\end{array}\right)=\frac{13!}{3!\cdot \left(13-3\right)!}=\frac{13!}{3!\cdot 10!}=\frac{{\cancel{10!}}^1\cdot 11\cdot {\cancel{12}}^2\cdot 13}{1\cdot {\cancel{2\cdot 3}}^1\cdot {\cancel{10!}}^1}=286$  

$\left(\begin{array}{c}13\\ 9\end{array}\right)=\frac{13!}{9!\cdot \left(13-9\right)!}=\frac{13!}{9!\cdot 4!}=\frac{{\cancel{9!}}^1\cdot {\cancel{10}}^5\cdot 11\cdot {\cancel{12}}^1\cdot 13}{{\cancel{9!}}^1\cdot 1\cdot {\cancel{2}}^1\cdot {\cancel{3\cdot 4}}^1}=715$  

$\left(\begin{array}{c}13\\ 10\end{array}\right)=\frac{13!}{10!\cdot \left(13-10\right)!}=\frac{13!}{10!\cdot 3!}=\frac{{\cancel{10!}}^1\cdot 11\cdot {\cancel{12}}^2\cdot 13}{{\cancel{10!}}^1\cdot 1\cdot {\cancel{2\cdot 3}}^1}=286$  

Zauważamy, że:

$78<286<715$  

Zatem:

$\left(\begin{array}{c}13\\ 2\end{array}\right)<\left(\begin{array}{c}13\\ 3\end{array}\right)=\left(\begin{array}{c}13\\ 10\end{array}\right)<\left(\begin{array}{c}13\\ 9\end{array}\right)$  

Zdanie A i B jest prawdziwe.

Zdanie C jest nieprawdziwe.

Zauważamy, że:

$78:13=6$  

$286:13=22$  

$715:13=55$  

Zdanie D jest prawdziwe.

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Odp. C.